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FRM Part I · FRM Exam Part I · Hypothesis Testing

A multiple regression with 3 explanatory variables and 44 observations gives a coefficient estimate of 1.20 with standard error 0.50. Test H0: coefficient = 0 (two-sided). Critical t values with 40 degrees of freedom are 2.021 (5% level) and 2.704 (1% level). Which statement is correct?

With 40 degrees of freedom, the t-statistic of 2.40 exceeds the 5% critical value of 2.021 but falls short of the 1% value of 2.704. The coefficient is significant at 5% but not at 1%, and the 95% interval of about 0.19 to 2.21 excludes zero.

  1. At = 2.40; reject at 5% but not at 1%; the 95% confidence interval excludes zeroCorrect
  2. Bt = 2.40; reject at both 5% and 1%
  3. Ct = 2.40; do not reject at either level because df = 44
  4. Dt = 0.42; do not reject at either level

Explanation

Degrees of freedom are n - k - 1 = 44 - 3 - 1 = 40. The statistic is 1.20/0.50 = 2.40, which is above 2.021 but below 2.704. The 95% interval is 1.20 ± 2.021(0.50), about 0.19 to 2.21, which excludes zero. Inverting the ratio gives 0.42, which is wrong.

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